International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 1, Pages 1-8
Nowhere dense sets and real-valued functions with closed graphs
Department of Mathematics, University of Alberta, Edmonton T6G 2G1, Alberta, Canada
Received 19 April 1988; Revised 10 May 1988
Copyright © 1989 Ivan Baggs. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Closed and nowhere dense subsets which coincide with the points of
discontinuity of real-valued functions with a closed graph on spaces which are not
necessarily perfectly normal are investigated. Certain
subsets of completely
regular and normal spaces are characterized. It is also shown that there exists a
countable connected Urysohn space X with the property that no closed and nowhere
dense subset of X coincides with the points of discontinuity of a real-valued
function on X with a closed graph.